Effects of thermal stress slip on thermophoresis and photophoresis

An analysis is presented for the effects of thermal stress slip on the thermophoresis and photophoresis of a spherical aerosol particle. The Knudsen number is assumed to be moderately small so that the fluid motion is described by a near-continuum slip-flow model with a temperature jump, a thermal creep, a frictional slip, and a thermal stress slip at the particle surface. In the limit of small Peclet and Reynolds numbers, the energy and momentum equations governing the systems are solved analytically at steady state. Expressions for the migration velocities of the particle are obtained in simple closed forms for the cases of thermophoresis in a uniformly prescribed bulk-gas temperature gradient and of photophoresis subject to an intense light beam. Our results indicate that the effects of thermal stress slip can be significant when the Knudsen number is not too small or the particle is not too large. The effects of thermal stress slip can increase or decrease the thermophoretic mobility of the particle, depending on some properties of the particle and surrounding gas, but always augment the photophoretic mobility of the particle. The analytical predictions with the effects of thermal stress slip in general fit with available experimental data of thermophoretic and photophoretic forces on aerosol spheres better than those without the effects do.